NAME

       sgtrfs.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgtrfs (TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX,
           FERR, BERR, WORK, IWORK, INFO)
           SGTRFS

Function/Subroutine Documentation

   subroutine sgtrfs (characterTRANS, integerN, integerNRHS, real, dimension( * )DL, real,
       dimension( * )D, real, dimension( * )DU, real, dimension( * )DLF, real, dimension( * )DF,
       real, dimension( * )DUF, real, dimension( * )DU2, integer, dimension( * )IPIV, real,
       dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension(
       * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integer, dimension( * )IWORK,
       integerINFO)
       SGTRFS

       Purpose:

            SGTRFS improves the computed solution to a system of linear
            equations when the coefficient matrix is tridiagonal, and provides
            error bounds and backward error estimates for the solution.

       Parameters:
           TRANS

                     TRANS is CHARACTER*1
                     Specifies the form of the system of equations:
                     = 'N':  A * X = B     (No transpose)
                     = 'T':  A**T * X = B  (Transpose)
                     = 'C':  A**H * X = B  (Conjugate transpose = Transpose)

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           NRHS

                     NRHS is INTEGER
                     The number of right hand sides, i.e., the number of columns
                     of the matrix B.  NRHS >= 0.

           DL

                     DL is REAL array, dimension (N-1)
                     The (n-1) subdiagonal elements of A.

           D

                     D is REAL array, dimension (N)
                     The diagonal elements of A.

           DU

                     DU is REAL array, dimension (N-1)
                     The (n-1) superdiagonal elements of A.

           DLF

                     DLF is REAL array, dimension (N-1)
                     The (n-1) multipliers that define the matrix L from the
                     LU factorization of A as computed by SGTTRF.

           DF

                     DF is REAL array, dimension (N)
                     The n diagonal elements of the upper triangular matrix U from
                     the LU factorization of A.

           DUF

                     DUF is REAL array, dimension (N-1)
                     The (n-1) elements of the first superdiagonal of U.

           DU2

                     DU2 is REAL array, dimension (N-2)
                     The (n-2) elements of the second superdiagonal of U.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     The pivot indices; for 1 <= i <= n, row i of the matrix was
                     interchanged with row IPIV(i).  IPIV(i) will always be either
                     i or i+1; IPIV(i) = i indicates a row interchange was not
                     required.

           B

                     B is REAL array, dimension (LDB,NRHS)
                     The right hand side matrix B.

           LDB

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           X

                     X is REAL array, dimension (LDX,NRHS)
                     On entry, the solution matrix X, as computed by SGTTRS.
                     On exit, the improved solution matrix X.

           LDX

                     LDX is INTEGER
                     The leading dimension of the array X.  LDX >= max(1,N).

           FERR

                     FERR is REAL array, dimension (NRHS)
                     The estimated forward error bound for each solution vector
                     X(j) (the j-th column of the solution matrix X).
                     If XTRUE is the true solution corresponding to X(j), FERR(j)
                     is an estimated upper bound for the magnitude of the largest
                     element in (X(j) - XTRUE) divided by the magnitude of the
                     largest element in X(j).  The estimate is as reliable as
                     the estimate for RCOND, and is almost always a slight
                     overestimate of the true error.

           BERR

                     BERR is REAL array, dimension (NRHS)
                     The componentwise relative backward error of each solution
                     vector X(j) (i.e., the smallest relative change in
                     any element of A or B that makes X(j) an exact solution).

           WORK

                     WORK is REAL array, dimension (3*N)

           IWORK

                     IWORK is INTEGER array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Internal Parameters:

             ITMAX is the maximum number of steps of iterative refinement.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 208 of file sgtrfs.f.

Author

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